On the generalized continuity equation

TL;DR

This paper introduces a generalized continuity equation derived using quaternions, demonstrating its compatibility with fundamental quantum and relativistic equations and highlighting its implications for electron transport.

Contribution

The paper presents a novel quaternion-based generalized continuity equation that unifies and extends traditional equations, maintaining Lorentz invariance and impacting electron transport understanding.

Findings

Compatible with Dirac, Schrödinger, Klein-Gordon, and diffusion equations

Electron transport is governed by Schrödinger-like equations, not diffusion

The generalized equation is Lorentz invariant

Abstract

A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz invariant. The transport properties of electrons are found to be governed by Schrodinger-like equation and not by the diffusion equation.